Preheat the oven to 425°F (220°C). Line a baking sheet with parchment paper.
Divide the pizza dough into 4 equal portions. Roll each portion into an 8-inch circle on a lightly floured surface.
Spread 2–3 tablespoons of pizza sauce on half of each dough circle, leaving the edges clear.
Layer with mozzarella cheese, ricotta, pepperoni or sausage, bell peppers, and olives.
Fold the dough over the filling to form a half-moon shape. Press and seal the edges firmly using a fork.
Place calzones on the prepared baking sheet. Brush the tops with beaten egg for a golden finish.
Cut small slits on top of each calzone to allow steam to escape.
Bake for 15–18 minutes, or until golden brown and crispy.
Brush with olive oil before serving, if desired. Serve warm with extra pizza sauce for dipping.